I watched my son shoot his first 6 deer with the .243. I don't recall any of them taking more than a few steps, needless to say I'm impressed with it. A buddy in western KS shoots his mulies with it and doesn't have issue. Fun gun to shoot as well.
I have heard good things about the Sierra Gameking 85 grain boat tail hollow point. As has been pointed out, pronghorn are small animals and don't require a super tough bullet to kill.
One point I would mention, from my experience the behavior of mortally wounded pronghorn is a little surprising. My son hit a buck at about 150 yards with a .25-06 117 grain Hornady. The buck just stood there -- seemingly totally unphased and undisturbed. I was watching from behind a bump of ground and assumed my son had missed on his first shot. About 10 seconds later the buck took a few steps forwards, seemed to tremble, fell down butt first and rolled over dead. The shot was well placed right behind the elbow of the front leg -- where the shoulder blade meets the lower leg. When I shot may doe pronghorn at 240 yards with a .243 100 grain Winchester Super-X bullet, again the pronghorn gave no indication of being hit. I shot quickly again. And then again. The doe dropped dead. I would guess my first shot hit home but I was too impatient/lacking confidence to wait. They don't always drop dead on the spot when hit well. Give them a few seconds if they aren't threatening to walk quickly out of range. If they are standing still you aren't taking any risks waiting a few seconds to see what happens.
243 with a 100 gr bullet for a pronghorn is more gun for the animal than a 338 Lapua with a 300 gr bullet is for an elk.
If you are thinking about shooting more than 200 yards, practice with it at longer ranges on windy days. The wind always seems to blow when hunting pronghorn.
I was at the range today. My .243 with Nosler Accubonds or Nosler BT groups perfectly at 200 yards. Dime size groups. I have to test at 300+ yards... but 200 yards, I can probably shoot off hand with confidence.
Even a little wind on a plastic tip bullet isn't too bad. When I shoot my lead ammo, the wind has a much greater effect.
She was shooting 100 grain partitions on the elk. I tried to buy her an ‘elk’ caliber but she turned up her nose at me since she had been using this BLR 243 since she was 14. It should be noted that AJ is very particular about her shots. Close and broadside, the elk have all been within a 100 yards.
.243 is a great caliber for antelope and deer and even elk, my daughter has used her's with 85 grain sierra game king boat tail hollow points to kill 3 mule deer bucks and a cow elk. What I have found is that bullet performance really depends on bullet placement, what I mean is if your shooting a lighter jacket bullet at 100 yards you should not aim for the shoulder as it will look like a 338 mag went thru it, as with that same bullet at 400 yards you may want to aim for the shoulder because there might not be enough energy left for it to expand unless it hits bone. Knowing what your bullet will do at given distances is key with any caliber.
FYI, back in the day my daughter used to shoot a 243 for antelope and deer. I started off with the Hornady SST 95 grain factory loads, and it shot ok. Switched to the cheap federal soft points 100 grain bullets and man, talk about groups. That gun loved those cheap federal soft points and they dropped antelope and deer like a hammer.
I used to use my 270 for deer and antelope, but after getting a 243 and toying with different bullets I found that the 90 gr Accubonds shot the best out it. Took it to Wyoming this year and dropped three antelope where they stood between 200 & 380 yards. A fourth fell to it after a buddy borrowed it when the scope came loose on his rifle. Now he's looking for a 243 and I'm only taking my 243 for deer and antelope in the future.
Ive shot 3 with 243 using 80 grain ttsx. 315 yards in the lungs, pass thru, drt. Just over 400 yards, lungs, pass thru drt. 548 yards, liver. Walked 20 yards and stopped, spine shot dropped it. My buddys son dumped a cow elk with 243 federal copper 80 grain at 300 yards no problem. 22-250 with 60 grain partition has worked awesome as well. As a side note, ive seen them run for miles and never recovered with a bad hit from a 3p0 mag. In the boiler room, almost anything will work fine